Algebra Ring and Field theory by Alireza Salehi Golsefidy

This PDF covers the following topics related to Rings and
Fields : A pseudo-historical note, More on subrings and ring
homomorphisms, The evaluation or the substitution map, Defining fractions, Using
the universal property of the field of fractions, An application of the first
isomorphism theorem, The factor theorem and the generalized factor theorems,
Gaussian integers, Irreducibility and zeros of polynomials,
Content of a polynomial with rational coefficients, An example on the mod
irreducibility criterion, Factorization: uniqueness, and prime elements, Ring of
integer polynomials is a UFD, Greatest common divisor for UFDs, Extension of
isomorphisms to splitting fields, Finite fields, etc.

**Author(s):** Alireza Salehi
Golsefidy, University of California San Diego

295 Pages